In a bowl, beat the eggs. Stir in the dill, scallion, Thai chile, fish sauce, pepper, and salt.

In a medium nonstick skillet, heat 1 tablespoon of the oil. Add the shallot and cook over moderately high heat until softened, about 2 minutes. Add the remaining 1 tablespoon of oil and, when it is hot, add the egg mixture. Cook, stirring, until the eggs are almost set, about 1 minute. Run a heatproof plastic spatula around the edge to loosen the omelet and cook undisturbed until golden brown on the bottom, about 30 seconds. Invert the omelet onto a plate and serve.